8.6: Example Two
- Page ID
- 54277
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A typical problem is to assign grades based on a typical grading standard.
Understand the Problem
For this example, the program will assign grades using the following grade scale:
| A | B | C | D | F |
|---|---|---|---|---|
| >=90 | 80 - 89 | 70 - 79 | 60 - 69 | <=59 |
The program will read three test scores, compute the average, and display the appropriate grade based on the average.
Create the Algorithm
The algorithm is the name for the ordered sequence of steps involved in solving the problem.
For this problem, the variables will be declared and an initial header displayed. Then, the test1, test2, and test3 values will need to be read from the user.
! declare variables ! reals -> test1, test2, test3 ! integer -> testave ! display initial header ! read the test1, test2, and test3 values
Next, the average can be calculated. The average will be converted to the nearest integer and, based on that, the appropriate grade can be determined and displayed. Formalizing this, the following steps can be developed.
! calculate the testave and convert to integer ! determine grade ! A - >= 90 ! B - 80 to 89 ! C - 70 to 79 ! D - 60 to 69 ! F - <= 59
For convenience, the steps are written as program comments.
Implement the Program
Based on the algorithm, the following program can be created.
program grades
! declare variables
implicit none
real :: test1, test2, test3
integer :: testave
! display initial header
write (*,*) "Grade Assignment Program"
write (*,*)
write (*,*) "Enter test 1, test 2 and test 3 values"
! read the test1, test2, and test3 values
read (*,*) test1, test2, test3
! calculate the average and convert to integer
testave = nint ((test1 + test2 + test3)/3.0)
! determine grade
! A→>=90,B→80-89,C→70-79,D→60-69,F→<=59
select case (testave)
case(90:)
write (*,*) "Grade is: A"
case(80:89)
write (*,*) "Grade is: B"
case(70:79)
write (*,*) "Grade is: C"
case(60:69)
write (*,*) "Grade is: D"
case(:59)
write (*,*) "Grade is: F"
end select
end program grades
The indentation is not required, but does help make the program easier to read.
Test/Debug the Program
Once the program is written, testing should be performed to ensure that the program works. The testing will be based on the specific parameters of the program.
In this example, each of the three possible values for the discriminant should be tested.
C:\mydir> grade Grade Assignment Program Enter test 1, test 2 and test 3 values 70 80 90 Grade is: B C:\mydir>
The program should be tested with a series of data items to ensure appropriate grade assignment for each grade. Test values for each grade should be entered for the testing.